Chemistry Reference
In-Depth Information
Now for our example of an HEUR gel the concentration used was 52.5 kgm
-3
so that we had a value of c/c*
¼
0.72. This means that we may consider
entanglements to be unlikely but that some closed loops are likely to have been
formed. This was confirmed experimentally by the experimental value of the
network modulus, G
Nexpt
, being linear with polymer concentration, indicating
no c
2
dependence. The way that the network modulus was measured experi-
mentally was by oscillation of the gel at frequencies much larger than the
reciprocal of the slowest relaxation time. The slowest relaxation process in-
volved the removal of a hydrophobe from a cluster and for this gel was t
8s
with G
Nexpt
¼
2.6 kPa. Now, in an ideal network of this type of polymer each
chain could be expected to form an elastic link. The number of chains per unit
volume is
B
n
c
¼
cN
A
M
n
ð
2
:
54
Þ
and so we calculate the network modulus as
G
Ncalc
¼
cRT
M
n
ð
2
:
55
Þ
where R is the gas constant. Hence, for this system we obtained:
G
Nexpt
G
Ncalc
¼
0
:
7
ð
2
:
56
Þ
which indicates that 30% of the polymer chains are ineffective as elastic links.
The aggregation number of the hydrophobes in the clusters has been shown to
be N
agg
B
6,
21
but the value may be as high as 20. This is much lower than that
found for the micellar clusters of common surface active agents (surfactants)
such as sodium dodecyl sulphate, SDS. The latter form spherical clusters at low
concentrations containing
74 hydrophobic chains.
22
When surfactants are
added to an HEUR solution, mixed clusters are formed and with SDS, N
agg
B
B
110,
23
which means that ellipsoidal micellar clusters are formed. This is to be
expected due to the mismatch in the lengths of the two types of hydrophobe
involved.
The situation with the HMHEC polymers is a little more complicated and we
can use their behaviour to illustrate the importance of network defects. There
are a small number of hydrophobes randomly grafted along a relatively stiff
chain and the hydroxyethyl cellulose is prepared by the degradation of a
naturally occurring polymer so the molecular weight distribution is broad.
However, rheological measurements are an integration over a very large
number of interactions and so give a good measure of the average. Also,
the hydrophobes are of a narrow size distribution and these dominate the
stress relaxation times because the disaggregation of these requires the most
energy and is therefore the slowest process. The aggregation number of the
hydrophobe cluster is important in defining the range of relaxation times
that we see. If the aggregation number is large (say N
agg
410), the local
